DUBLIN (AP) — Ireland will pay several hundred former residents of Catholic-run Magdalene laundries at least $45 million to compensate them for their years of unpaid labor and public shame, the government announced Wednesday following a decade-long campaign by former residents of the workhouses.

Justice Minister Alan Shatter apologized to the women — an estimated 770 survivors out of more than 10,000 who lived in the dozen facilities from 1922 to 1996 — that it had taken so long for them to receive compensation.

The move marked the latest step in a two-decade effort by Ireland to investigate and redress human rights abuses in its Catholic institutions.

Shatter’s decision came four months after a government-commissioned probe found that women consigned to the laundries were broadly branded ‘‘fallen’’ women.